Error estimation in whole bone microstrain measurement when using digital volume correlation

Abstract

Micro-CT scanning of murine femurs before and after uniaxial compression produce 3-dimensional images detailing changes within the bone micro-architecture. Digital volume correlation (DVC) is a mathematical technique used to determine strain within the bone volume, by tracing the dislocation of a pattern between the 3-dimensional images. Uncertainty in the microstrain calculated arises due to limitations in microscopy, the absence of a homogeneously distributed pattern within the bone volume, and inconsistency the methodology used to process the micro-CT scans and microstrain data. The uncertainty in strain was quantified as strain error (SE), measured by analyzing repeated micro-CT scans of an uncompressed bone. The Minimum SE quantified was 180-225 microstrains in accuracy (mean), with a 1100-2100 microstrain precision (standard deviation) in rats; 10-150 microstrains in accuracy, with a 1100-1700microstrain precision in mice. SE displays a regular random distribution throughout the bone volume, centered about 0 and showing strain in both tension and compression. The minimum SE is obtained by optimizing the DVC input parameters using a design of experiments (D0E). A sub-volume size of 43-55 voxels with a 50-75% volume overlap between consecutive steps of the DVC yielded the lowest SE at the highest strain resolution within the bone sub-volume. A strain error resolution (SER) of 2500 microstrains encapsulates over 90% of the SE and is chosen as the minimum strain value that is viable when evaluating microstrain from a compression test of the bone. Any strain within the SER limits are eliminated from a viable set of microstrain value, believed to either be error or minimally contributing to the macroscopic properties of the bone. SER of 2500 microstrain results in a displacement uncertainty of 9-11 um within the bone subvolume. A visual inspection of the repeated scans shows an uncertainty of 2.5 voxels between the 2 images when imaged at a nominal resolution of 4-5 um. The use of monochromatic x-rays (such synchrotron x rays) can increase resolution and reduce the signal-to-noise ratio in the CT scanning process, thus reducing the SE calculated by DVC.